OK, so SR 509 (and SSH 1V before it) headed south into downtown Des Moines. At the split between Marine View Drive and the Kent-Des Moines Road, originally (at least after the 1964 renumbering), SR 516 began heading east on the Kent-Des Moines Road. SR 509 turned right to head south on Marine View Drive, across the bridge over Saltwater State Park. Originally this segment was added to the state highway system in 1937. Anyway, originally, 509 curved left at Woodmont Drive. Then it took a right at 16th Ave S, and joined SR 99 where 16th Ave S meets Pacific Hwy/ SR 99.
This changed in 1992. The segment of SR 509 from junction 516, on Marine View Drive, Woodmont, and 16th was removed from state maintenance effective April 1, 1992. Now, officially 509 is concurrent with 516 from the corner of Marine View Drive and Kent-Des Moines Road to junction SR 99 at Midway. Then 509 (on paper) turns south and is concurrent with 99 until it splits off at Dash Point Road. However, as you pointed out, signage to this effect is almost completely non-existent, leading one to believe there is simply a gap in SR 509. But, as I was through the area recently, I saw an older (likely early 90's) sign on northbound Marine View Drive (ex-509), just before the light at Kent-Des Moines Road that says 509 north to the left, 509 south to the right, and begin 516 east to the right. I took a picture of this sign, but I have yet to upload it to Flickr.